A Comprehensive Analysis of the Relation between Intermittency and Dissipation in Non-Homogeneous Turbulent Flows
Abstract
A recent study of various turbulent flows showed that intermittency and dissipation exhibit consistent scaling behavior beyond homogeneous isotropic turbulence (HIT). For turbulent wakes, grid turbulence, and a turbulent jet, the dissipation parameter Cε and intermittency parameter μ vary while their product remains constant, independently of the Reynolds number Reλ. Here, we extend this result from centerline hot-wire measurements to non-centerline data, including regions with significant shear. We identify two additional relations: (γ−1)Cε remains constant, where γ is the absolute inertial-range spectral slope, and γ varies linearly with the Kolmogorov parameter Ck. The main constraint is that the large-scale increment probability density function is Gaussian, indicating random large-scale driving. These relations reduce the varying quantities Cε, μ, γ, and Ck to three constants and define a turbulence state that can be characterized by any one of these parameters, independently of shear, flow type, or Reynolds number. We further show that, for a given flow configuration, Cε depends on Reλ and turbulence intensity TI. Because the four parameters vary over broad ranges around their nominal HIT values, we interpret this framework as a generalization of HIT to inhomogeneous turbulence. Extensive robustness tests show that the results are insensitive to the specific post-processing method. We also analyze their streamwise and spatial evolution and show that a measured Cε can be used to predict μ, γ, and Ck within quantified uncertainty. The framework thus links key leading-order features of turbulence while recovering established HIT trends.
Versions
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BibTeX
@misc{schmitt2026comprehensive,
title = {{A Comprehensive Analysis of the Relation between Intermittency and Dissipation in Non-Homogeneous Turbulent Flows}},
author = {F. H. Schmitt and J. Peinke and M. Obligado},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14667},
eprint = {2609.14667},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14667},
}
RIS
TY - UNPB
TI - A Comprehensive Analysis of the Relation between Intermittency and Dissipation in Non-Homogeneous Turbulent Flows
AU - F. H. Schmitt
AU - J. Peinke
AU - M. Obligado
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14667
UR - https://arxiv.org/abs/2609.14667
AB - A recent study of various turbulent flows showed that intermittency and dissipation exhibit consistent scaling behavior beyond homogeneous isotropic turbulence (HIT). For turbulent wakes, grid turbulence, and a turbulent jet, the dissipation parameter C_ε and intermittency parameter μ vary while their product remains constant, independently of the Reynolds number Re_λ. Here, we extend this result from centerline hot-wire measurements to non-centerline data, including regions with significant shear. We identify two additional relations: (γ−1)C_ε remains constant, where γ is the absolute inertial-range spectral slope, and γ varies linearly with the Kolmogorov parameter C_k. The main constraint is that the large-scale increment probability density function is Gaussian, indicating random large-scale driving. These relations reduce the varying quantities C_ε, μ, γ, and C_k to three constants and define a turbulence state that can be characterized by any one of these parameters, independently of shear, flow type, or Reynolds number. We further show that, for a given flow configuration, C_ε depends on Re_λ and turbulence intensity TI. Because the four parameters vary over broad ranges around their nominal HIT values, we interpret this framework as a generalization of HIT to inhomogeneous turbulence. Extensive robustness tests show that the results are insensitive to the specific post-processing method. We also analyze their streamwise and spatial evolution and show that a measured C_ε can be used to predict μ, γ, and C_k within quantified uncertainty. The framework thus links key leading-order features of turbulence while recovering established HIT trends.
ER -